1. Field of the Invention
My invention relates generally to methods for measurement and display of complex sinusoidal impedance and, more specifically, to the display of complex sinusoidal electrical impedance in biological tissues at many frequencies.
2. Background of the Invention
The concept of a complex impedance for an object is well-known in the acoustical, electrical, and mechanical arts. An object impedance is usually defined as the ratio of a motivating excitation divided by a resulting object response at a single sinusoidal frequency, .omega.. For example, the complex mechanical impedance, Z, of a structure can be expressed as the ratio of a sinusoidal excitation force, F, to the resulting sinusoidal velocity, V, of the structure at the point of application of the excitation force, that is: EQU Z(.omega.)=F(.omega.,t)/V(.omega.,t)
The complex nature of such a driving point impedance arises from the time delay, d, of the peak sinusoidal velocity, V, with respect to the peak sinusoidal excitation force, F. This is commonly expressed in the following form: ##EQU1## Where: .omega.=angular sinusoidal frequency in radians/second, and
.omega.d=phase delay of V with respect to F in radians.
This concept of complex object impedance at a single sinusoidal frequency can be used to express a mechanical ratio of force to velocity, an acoustic ratio of pressure to displacement, an electrical ratio of voltage to current, a thermal ratio of temperature differential to heat flow, an electromagnetic ratio of electric field to magnetic field, and so forth as is well-known in the art.
The classical method known in the art for measuring and displaying values of complex object impedance requires the measurement of the response of the object to an applied excitation at a single sinusoidal frequency. For instance, the complex electrical impedance of an object can be determined by applying a sinusoidal voltage to the object and measuring the resultant sinusoidal current flow through the object. The electrical object impedance magnitude may then be determined as the ratio of the root-mean-square (RMS) voltage and current values and the object impedance phase angle may be determined as the delay in radians of the peak sinusoidal current with respect to the peak sinusoidal voltage. The real and imaginary components of the complex object impedance may be determined from impedance magnitude and phase angle according to: EQU Resistance=Re[Z]=R=.vertline.Z.vertline.cos.theta., where .theta.=.omega.d, EQU Reactance=Im[Z]=X=.vertline.Z.vertline.sin.theta., and EQU Impedance=Z=R+iX
A number of problems are known in the impedance measurement art that lead to errors and ambiguities when the values of complex object impedance are measured and displayed. The most significant problem arises from the requirement that the complex impedance be determined at a single sinusoidal frequency. The presence of other frequency components in the excitation and response signals lead to errors in the displayed complex impedance. Practitioners in the art have proposed analog filtering techniques and special excitation signal generation methods for minimizing the errors arising from such unwanted signal components. However, analog filter devices are subject to calibration errors, thermal drift and other problems, which introduce amplitude and phase errors in the excitation and response signals. These phase errors often become severe at high values of reactance (imaginary impedance) and can completely overwhelm the character of the complex impedance under measurement.
Other serious limitations to accurate complex impedance display are well-known in the art. High impedance magnitudes require the determination of a ratio between a large excitation signal and a very small response signal, leading to errors arising from the presence of noise in the small response signal. Practitioners propose the use of very high excitation signal amplitudes to overcome the effects of such noise, but high levels of excitation signal may damage or destroy the object to which the excitation signal is applied. This is especially problematic in cases where the object under measurement is living biological tissue.
Another problem arising from the single frequency nature of complex object impedance is the difficulty in measuring complex object impedance at several frequencies over a wide frequency range. Because signal filters are necessary to ensure sinusoidal purity, these filters must be retuned to permit impedance display at other sinusoidal frequencies. The range of frequencies over which analog filters can be retuned is very limited, often to a few octaves. Alternatively, individual signal filters can be provided for each measurement frequency, but this approach seriously limits the number of frequencies for which complex object impedance can be displayed in any particular situation.
The analog signal filtering and display components used in the art are subject to calibration drift resulting from thermal changes and variations in operating region. This problem leads to a requirement for frequent recalibration to minimize complex impedance display errors, thereby preventing the rapid and effective measurement of complex object impedance at several frequencies.
The use of balanced bridge impedance measurement techniques known in the art can overcome many of the deficiencies of the signal ratio measurement methods mentioned above. However, balanced bridge techniques require a well calibrated impedance standard and are limited in practical application to the determination and display of electrical impedances. Moreover, the standard analog bridge components are presumed to be linear with respect to signal amplitude, which is an inaccurate presumption in most applications. This presumption leads to errors in display of complex object impedance that arise with changes in excitation signal level. Finally, balanced bridge techniques are unsuitable for accurate complex impedance determination over a wide frequency range and, in fact, are often limited to a single sinusoidal calibration frequency at a single excitation signal amplitude.
Another problem well-known in the art arises from the effects of small errors in impedance phase angle at angle values approaching .pi./2 radians (90.degree.). At these phase angles, the tangent function approaches infinity and extremely small errors in phase angle cause extremely high errors in one or both of the complex impedance components. A number of clever techniques have been proposed by practitioners in the art to overcome this problem, but most rely on the thermal discrimination between real and imaginary electrical power flow in a circuit and are unsuitable for use over a range of frequencies or with nonelectrical impedance measurement.
Yet another problem with classical impedance measurement and display techniques is the difficulty in simultaneously determining impedance at widely separated frequencies. This problem arises when the object under measurement experiences changes in impedance properties as a result of the application of the excitation signal. An example of this is the well-known tendency of an object to increase in temperature in response to the application of an electrical voltage. When the complex object impedance is a function of object temperature, then the measurement of complex impedance at one frequency will heat the object and create errors in the measurement of complex impedance at another frequency because of the difficulty in measuring such impedances simultaneously. One solution is to use a plurality of impedance measurement and display devices to simultaneously measure complex object impedance at a plurality of sinusoidal frequencies, but this method is cumbersome and not practical for large numbers of measurement frequencies.
These and other related difficulties with accurate display of complex object impedance are exacerbated in the situation where the object of interest is living biological tissue. The measurement and display of complex electrical impedance in biological tissue has been of interest since the late 1800's By 1921 it had been well-supported that the living cell had a well-conducting interior surrounded by a relatively impermeable, poorly conducting membrane. In 1925, Fricke reported (Fricke, H., Mathematical Treatment of the Electrical Conductivity and Capacity of Disperse Systems, Phys. Rev. 26:678-681, 1925) that at low frequency (LF) currents, there was little conduction through the cell because of high membrane capacitance. Thus, Fricke argued that conduction occurs primarily in the extracellular fluid (ECF) compartment and, at a sufficiently high frequency (HF), the current is shunted through the cell membrane and conducts through both the ECF and intracellular fluid (ICF).
Knowledge of biological material properties has been obtained through complex impedance measurements across various cells, suspensions, fibers, eggs and tissues. Of primary significance were the discoveries of cell membrane capacitance, the beta dispersion region, the additional regions of dispersions for cell suspensions, and Maxwell's mixture theory for analyzing the impedance measurement data.
In general, all cells and tissues may be expected to show three major dispersion regions in relation to frequencies (.alpha., .beta. and .gamma.). Of particular interest is the central .beta.-dispersion region, which is explained by the dielectric capacity of the cell membranes. The .alpha. and .gamma. regions are attributed to a surface conductance and to intracellular components. The .beta. region can be expressed in either a simple or complex equivalent circuit orientation form, where parallel resistance (R.sub.P) reflects extracellular fluid (R.sub.ccw) and the series orientation corresponds to intracellular fluid resistance (R.sub.icw) and cell membrane capacitance (C.sub.M). The equivalent circuit used in the Maxwell analysis must give the semi-circular relation (impedance and admittance loci) between the real and imaginary components of the impedance as applied frequency is varied, according to Cole (Cole, K. S., Membrane, Ions and Impulses, University Press, Berkeley, 1968).
An early attempt to apply this concept was made by Thomassett (Thomassett, A., Bio-Electrical Properties of Tissues, Lyon Med. 209:1325-1352, 1963), who measured simple impedance at high (100 kHz) and low (1 kHz) frequency currents using a two-wire technique. The high correlations of high frequency impedance to total body water (TBW) and low frequency impedance to extracellular fluid gave further support to the membrane and dispersion theories. However, Thomassett's approach did not develop into a practical clinical method.
Using a four-wire configuration, Hoffer, et al. (Hoffer, E., Meador, C., Simpson, C., Correlation of Whole-Body Impedance with Total Body Water Volume, J. Appl. Physio. 17, 4:531-534, 1969) reported a high correlation between measured TBW and TBW estimated by Ht.sup.2 /Resistance at 100 kHz. However, Hoffer, et al. reported that their high standard deviations implied that further development was necessary to make the technique a practical clinical method.
A decade later, Nyboer, et al. (Nyboer, J., Liedtke, Reid, K., Gesert, W., Nontraumatic Electrical Detection of Total Body Water and Density in Man, Proceedings of the VI ICEBI, 381-384, 1983) found that measurements of electrical resistance at 50 kHz, combined with subject weight, height and age, could accurately determine body density (fat and lean) in human subjects These relationships were based on the assumption that a strong relationship must exist between Fat-Free Mass (FFM) and TBW estimated by impedance because FFM tissue is consistently hydrated. Following the Nyboer, et al. work, a tremendous amount of interest arose for the impedance method.
Since the Nyboer, et al. presentation, many practitioners have sought to validate the single frequency impedance method of estimating human body composition in various populations (Lukaski, H. C., Johnson, P. E., Bolonchuk, W. W., Lykken, G. I., Assessment of Fat-Free Mass Using Bioelectrical Impedance Measurements of the Human Body, Am. J. Clin. Nutr., 41:810-817, 1985; Segal, K., Van Loan, M., Fitzgerald, P., Hodgdon, J. A., Van Itallie, T. B., Lean Body Mass Estimation by Bioelectrical Impedance Analysis: a Four Site Cross-Validation Study, Am. J. Clin. Nutr. 47:7-14, 1988; and Kushner, R., Kunigk, A., Alspaugh, M., Andronis, P., Leitch, C., Schoeller, D., Validation of Bioelectrical-Impedance Analysis as a Measurement of Change in Body Composition in Obesity, Am. J. Clin. Nutr. 52:219-23, 1990). Results have been mostly positive for normal subjects but the predictions of FFM have been far less precise in the clinical and abnormal population groups. Although impedance data continued to correlate highly to TBW, the underlying assumption that FFM is consistently hydrated has recently been found to be incorrect (Deurenberg, P., Westtrate, J. A., Hautvast, J., Changes in Fat-Free Mass During Weight Loss Measured by Bioelectrical Impedance and by Densitometry, Am. J. Clin. Nutr. 49:33-6, 1989). Furthermore, increased awareness of the usefulness of the multi-frequency measurements has led to a general belief that the single frequency method is too simplistic and limiting (Cohn, S., How Valid are Bioelectrical Impedance Measurements in Body Composition Studies?, Am. J. Clin. Nutr. 42:889-890, 1985). Criticism was also raised over the clinical usefulness of TBW in view of frequently encountered fluid shifts between the ICW and ECW. Van Itallie, et al. (Van Itallie, T., Segal, K., Nutritional Assessment of Hospital Patients: New Methods and New Opportunities, Am. J. Hum. Bio 1:205-8, 1989) assert that a practical method of discerning the ICW from the extracellular fluid would offer much greater utility and could profoundly influence hospital patient care and diagnosis.
Recently, several practitioners (Lukaski, H. C., Bolonchuck, W. W., Estimation of Body Fluid Volumes Using Tetrapolar Bioelectrical Impedance Measurements, Aviat. Space Environ., Med Dec., 1163-69, 1988 and McDougall, D., Shizgal, H., Body Composition Measurements from Whole Body Resistance and Reactance, Surgical Forum, 36:43-44, 1986) have proposed using the reactive element in a complex single frequency (50 kHz) impedance measurement to accurately discriminate the extracellular from the cellular mass. However, the use of multi-frequency measurements of impedance remains the technique of choice (Boulier, A., Fricker, J., Thomassett, A. L., Apfelbaum, M., Fat-Free Mass Estimation by Two-Electrode Impedance Method, Am. J. Clin. Nutr. 52:581-5, 1990).
Several practitioners have continued to test the Thomassett technique (Jenin, P., Lenoir, J., Roullet, C., Thomassett, A., Ducrot, H., Determination of Body Fluid Compartments by Electrical Impedance Measurements, Aviat Space Environ. Med. 46:152-5, 1975; Settle, R. G., Foster, K. R., Epstein, B. R., Mullen, J. L., Nutritional Assessment: Whole Body Impedance and Body Fluid Compartments, Nutr. Cancer, 2:72-80, 1980; and Tedner, B. T., Equipment Using an Impedance Technique for Automatic Recording of Fluid-Volume Changes During Hemodialysis, Med. & Biol. Eng. & Comput. 21:285-290, 1983). These practitioners use the ratio of high to low frequency simple impedance to reflect fluid compartment volume, the normal and abnormal fluid ratio, and fluid compartment change. The major problem reported for this technique is that the simple HF/LF ratio is too simplistic because volume is not determined and the compartment actually affected is not identified, although a change in ratio does reflect a change in compartmental volume. Furthermore, practitioners note that the lack of two-frequency simple impedance instrumentation prevents further exploration of this approach.
Because living tissue is mainly affected by ECF at frequencies below the .beta.-dispersion region, and ECF, C.sub.M and ICF at frequencies above this region, Kanai, et al. (Kanai, H., Haeno, M., Sakamoto, K., Electrical Measurements of Fluid Distribution of Legs and Arms, Med. Prog. Tech. 12:159-170, 1987) Computed the component values of the human muscle tissue equivalent circuit model (R.sub.ecw, R.sub.kw, and C.sub.M) known in the art. By mathematically analyzing the complex impedance measurements at multiple frequencies, Kanai, et al. obtained information specific to the ECW and ICW. However, others have been unable to replicate this advanced approach because of the lack of necessary and appropriate complex impedance instrumentation.
Expanding the prior art human body composition model from a simple two-compartment (lean/fat) model to a more complex model including ICF and ECF, protein, mineral and fat, creates a clearly-felt need for new and improved assessment techniques. This need has been unmet, until now because of the lack of appropriate complex impedance instrumentation and the lack of the necessary degree of sophistication in the associated measurement and analysis methods. This situation has inhibited the progress of this promising technology.
Increased use of diuretic drugs, fluid monitoring difficulties in intensive care, and the shrinking cell mass and expanding ECF that accompany most systemic wasting diseases and malnutrition has led to a well-recognized need for effective multi-frequency bioimpedance instrumentation in support of the compartmental approach to body fluid assessment. These unresolved problems and deficiencies are clearly felt in the art and are solved by my invention in the manner described below.